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Quantification Techniques for Arterial Blood Flow and the Left Atrium
by
Nikhil Jha
A thesis submitted to the Graduate Faculty of Auburn University
in partial fulfillment of the requirements for the Degree of
Master of Science
Auburn, Alabama August 2, 2014
Keywords: Magnetic Resonance Imaging, Pulse Wave Velocity, Arterial Blood Flow, Left Atrial Volumetric Analysis.
Copyright 2014 by Nikhil Jha
Approved by
Thomas S. Denney, Jr., Chair, Professor of Electrical and Computer Engineering Stanley J. Reeves, Professor of Electrical and Computer Engineering
Gopikrishna Deshpande, Assistant Professor of Electrical and Computer Engineering
ii
Abstract
Cardiovascular dysfunction is a major cause of morbidity and mortally. As such, the
characterization of the heart and surrounding vessels has a high clinical significance. The advent of
cardiac magnetic resonance imaging (MRI) has provided an effective and efficient, noninvasive method
of looking at the cardiovascular system.
This thesis investigates the application of MRI in the quantification of two particular aspects of
the cardiovascular system: arterial blood flow and the left atrium (LA).
The use of pulse wave velocity (PWV) in flow quantification is explored. The majority of
prevalent techniques use landmarks in the time-domain to calculate PWV. However, this presents
problems with reliability due to the low temporal resolution of MRI flow data. A frequency-domain based
approach through the use of the Fourier transform is investigated. This method is shown to be effective in
minimizing errors found in the time-domain calculations.
Dual-contour propagation is a post-processing technique used to produce contours. This is done
through the propagation of manually drawn end-diastole (ED) and end-systole (ES) contours throughout
the cardiac cycle. The method has been previously validated in regards to its applicability for ventricular
data. The application of this technique with LA MRI images is considered and shown to be a valid
propagation method.
Finally, different approaches to volumetric quantification of the LA are explored. Issues are
raised with the accepted serial short-axis and area-length calculation methods and a new virtual short-axis
method is proposed. This method seeks to compensate for the inaccurate geometric assumptions made by
the area length method whilst avoiding the time intensive use of the short-axis in quantification. This
method is shown to be effective and efficient method for volumetric analysis.
iii
Acknowledgments
First and foremost, I would like to thank Dr. Thomas S. Denney Jr. From my time as an
undergraduate, he has afforded me great opportunities through the Auburn University MRI Research
Center. From his instruction on MATLAB to teaching me to use the MRI machines, he has made this
work possible. His wisdom and insight have guided me in my work and helped me explore the field of
cardiovascular MRI. His enthusiasm for the research has helped cultivate a profound fascination with the
subject.
Dr. Nouha Salibi has been both an invaluable resource and a constantly uplifting presence during
my time at Auburn. Her comprehensive knowledge of MRI has helped me overcome many roadblocks.
I would also like to thank my advisory committee: Dr. Gopikrishna Desphande and Dr.Stanley J.
Reeves for their support in my thesis and my work.
Alongside them, the doctors and researchers at the University of Alabama at Birmingham School
of Medicine have helped make this work possible. Their help and guidance, particularly that of Dr.
Himanshu Gupta and Dr. Steven S Lloyd, has been vital to my work in cardiovascular research.
My coworkers and labmates: Wei Zha, Chun Schiros, Ming Li, Wayne Duggan, and Xiaoxia
Zhang, have been absolutely incredible. Both professionally and personally, they have created an
environment in which I have truly loved working. I would especially like to thank Wei for her support
and immense involvement when I first joined the research group. Without this help, I would still be trying
to figure out coding in MATLAB. I also want to particularly thank Xiaoxia Zhang. Without her
sacrificing nights and weekends to spend hours scanning subjects, I would not have been able to obtain
data.
iv
I would like to thank Ms. Linda Baressi and the workers at the Broun Hall Machine Shop.
Working there has allowed to me to step back and take a breath at times of incredible frustration. Miss
Linda is an incredible and constant source of support and inspiration.
My family, my parents and brother, have provided unconditional love and support in all my
endeavors. Without their presence in my life and the wonderful upbringing they provided, I would not be
who I am and certainly not have been able to get thus far.
Finally, I would like to thank my grandparents, Dr. Ashutosh Mishra and Dr. Shankuntala
Mishra. Their presence during my time at Auburn has brought me unspeakable joy. Their immense love,
constant support, and unending encouragement have been a driving force in helping me overcome my
obstacles. I dedicate this thesis to them.
v
Table of Contents
Abstract ...................................................................................................................................................... ii
Acknowledgments ..................................................................................................................................... iii
List of Tables .......................................................................................................................................... viii
List of Illustrations .................................................................................................................................... ix
List of Abbreviations ................................................................................................................................ xi
Chapter 1: Introduction ............................................................................................................................... 1
Chapter 2: Overview of the Cardiovascular System ................................................................................... 3
2.1 The Heart ................................................................................................................................. 3
2.1.1 Cardiac Anatomy ............................................................................................................... 3
2.1.2 Cardiac Physiology ............................................................................................................ 4
2.2 Blood Vessels .......................................................................................................................... 5
2.2.1 Vascular Anatomy ............................................................................................................. 5
2.2.2 Vascular Physiology .......................................................................................................... 6
2.3 Cardiovascular Dysfunction ..................................................................................................... 7
Chapter 3: Overview of Cardiovascular Magnetic Resonance Imaging ..................................................... 9
3.1 Fundamentals of Magnetic Resonance Imaging ...................................................................... 9
3.2 Cardiac Magnetic Resonance Imaging .................................................................................. 11
3.2.1 Cine Cardiac MRI ............................................................................................................ 11
3.2.2 Tagged Cardiac MRI ....................................................................................................... 13
3.2.3 Phase Contrast Cardiac MRI ........................................................................................... 14
vi
Chapter 4: Pulse Wave Velocity and the Quantification of Arterial Flow ................................................ 15
4.1 Arterial Flow and Pulse Wave Velocity ................................................................................ 15
4.1.1 Overview of Arterial Flow ............................................................................................... 15
4.1.2 Significance of Pulse Wave Velocity .............................................................................. 16
4.1.3 Calculation of Pulse Wave Velocity ................................................................................ 18
4.2 Contouring Cardiac Flow Images and Distance Calculation ................................................. 19
4.3 Common Methods for Transit Time Determination .............................................................. 20
4.3.1 Peak Analysis Using a Quadratic Fit ............................................................................... 21
4.3.2 Cubic Spline Interpolation of PC MRI Waveforms ......................................................... 23
4.3.3 Onset Time Analysis........................................................................................................ 24
4.3.4 Peak Acceleration Analysis ............................................................................................. 25
4.3.5 Issues with Transit Time Determination in the Time Domain ........................................ 26
4.4 Alternative Method for Transit Time Determination Using the Frequency Domain ............. 28
4.5 Comparison of Quantification Methods in Pulse Wave Velocity Calculation ...................... 30
4.5.1 Methodology .................................................................................................................... 30
4.5.2 Results ............................................................................................................................. 31
4.5.3 Discussion ........................................................................................................................ 32
4.5.4 Conclusion ....................................................................................................................... 32
4.6 Further Work .......................................................................................................................... 33
Chapter 5: Quantification of the Left Atrium ........................................................................................... 34
5.1 Overview of the Left Atrium ................................................................................................. 34
5.2 Contour Propagation for the Left Atrium .............................................................................. 36
5.2.1 Dual-Contour Propagation ............................................................................................... 37
5.2.2 Method ............................................................................................................................. 38
5.2.3 Results ............................................................................................................................. 39
5.2.4 Discussion ........................................................................................................................ 40
vii
5.3 Accepted Methods for Left Atrial Quantification .................................................................. 41
5.3.1 Serial Short-Axis Method ................................................................................................ 41
5.3.2 Areal-Length Method ...................................................................................................... 41
5.4 Proposed Virtual Short-Axis Method for Left Atrial Quantification ..................................... 42
5.5 Validation of the Virtual Short-Axis Method ........................................................................ 43
5.5.1 Method ............................................................................................................................. 43
5.5.2 Results ............................................................................................................................. 44
5.5.3 Discussion ........................................................................................................................ 45
5.6 Conclusion and Further Work ................................................................................................ 46
Chapter 6: Summary and Future Work ..................................................................................................... 48
References ............................................................................................................................................... 50
viii
List of Tables
Table 4.1: Comparison of PWV calculations from various methods ........................................................ 31
Table 5.1: Least-squares estimates of mean difference in LA VTCs between scans ................................ 40
Table 5.2: Least-squares estimates of mean differences between AL and VSA to SSA VTCs ................ 45
Table 5.3: Least-squares estimate of difference of the absolute disparity of AL and VSA to SSA ......... 45
ix
List of Figures
Figure 2.1: Anatomy of a Normal Heart ................................................................................................... 4
Figure 2.2: The Cardiac Cycle .................................................................................................................. 5
Figure 2.3: Blood Vessel Structure ........................................................................................................... 6
Figure 2.4: Circulatory System ................................................................................................................. 7
Figure 3.1: Precession of a proton ........................................................................................................... 10
Figure 3.2: Slice prescriptions for cMRI ................................................................................................. 12
Figure 3.3: Cine and corresponding tagged MR images as ED and ES .................................................. 13
Figure 3.4: Output of PC MRI of transected aorta ................................................................................... 14
Figure 4.1: Transmission line model for systemic circulation ................................................................. 16
Figure 4.2: Image of contouring the aorta using CAAS MR Flow .......................................................... 19
Figure 4.3: Images depicting distance determination for PWV calculation ............................................ 20
Figure 4.4: Flow plots for peak analysis method ..................................................................................... 22
Figure 4.5: Comparison of polynomial and spline interpolation ............................................................. 23
Figure 4.6: Flow plots depicting spline interpolation .............................................................................. 24
Figure 4.7: Flow plots for onset time analysis ......................................................................................... 25
Figure 4.8: Flow plots for analysis using peak acceleration method ..................................................... 26
Figure 4.9: Comparison of flow data from catheterization with PC MRI ................................................ 27
Figure 4.10: Plots of linear phase characteristics from frequency domain method .................................. 29
Figure 5.1: 3D models of LA and LV created with MATLAB ................................................................ 35
Figure 5.2: LA pressure-volume loop over cardiac cycle ......................................................................... 35
Figure 5.3: Propagation scheme for LA using dual-contour propagation ................................................. 38
x
Figure 5.4: LA VTCs computed using SSA and AL with propagated contours ....................................... 39
Figure 5.5: Illustration of area-length calculation method ........................................................................ 42
Figure 5.6: VTCs computed with SSA, AL, and VSA methods ............................................................... 44
xi
List of Abbreviations
2ch Two-Chamber
4ch Four-Chamber
AL Area-Length
AV Atrioventricular
cMRI Cardiac Magnetic Resonance Imaging
CT Computed Tomography
ED End-Diastole
ES End-Systole
IRB Institutional Review Board
LV Left Ventricle
LA Left Atrium
MPA Main Pulmonary Artery
MRI Magnetic Resonance Imaging
MV Mitral Valve
NIH National Institute of Health
NMR Nuclear Magnetic Resonance
NRR Non-Rigid Registration
PC Phase Contrast
PET Positron Emission Tomography
xii
PWV Pulse Wave Velocity
RA Right Atrium
RF Radio Frequency
ROI Region of Interest
RPA Right Pulmonary Artery
RV Right Ventricle
SA Short-Axis
SSA Serial Short-Axis
SPAMM Spatial Modulation of Magnetization
VSA Virtual Short-Axis
VTC Volume-Time Curve
1
Chapter 1
Introduction
The term cardiology often invokes the image of the human heart and its four chambers. The
surrounding vessels, however, play an integral role and, together with the heart, form the cardiovascular
system. In a system, the characteristics of a specific component impact the other components. This is no
different for the cardiovascular system. The characteristics and dysfunctions of individual anatomies have
a cascading affect and cause changes in the rest of the cardiovascular system. It is important to recognize
that the characteristics of the individual anatomical components are not static. As they are composed of,
among other things, various muscle and elastic tissues, their attributes change in response to variations in
pressure, encompassed blood volume, etc. The heart remodels with age and disease, the chambers
changing in size and shape; the arteries can lose elasticity and harden; there are changes in blood flow
around the body. As such, it is important to quantify the relationships between the various anatomies of
this system and how their overall characteristics change with the onset of physiological dysfunction
concentrated on one or more of the components. This is further compelling due to the crucial role that the
cardiovascular system plays in overall health.
However, before being able to characterize the overall cardiovascular system, it is necessary to
quantify the individual components. With the advent of noninvasive imaging technology, it has become
possible to observe, quantify, and characterize the behavior of the various chambers and vessels in vivo.
Magnetic resonance imaging (MRI) has been shown to be one of the most effective tools in achieving
this. It has, in fact, been used extensively in both research and clinical settings.
There has been extensive work to quantify some targeted anatomies such as the left ventricle
(LV). Less work has been done to effectively measure some of the other components of the
cardiovascular system. As more knowledge arises about them, the quantification of these components has
become significant. In this thesis, the focus is on the methods for processing and quantification for two
specific anatomical structures: the arterial system and the left atrium (LA).
2
In regards to the arterial system, the prevalent methods for blood flow quantification are
discussed and an alternative method is presented. These methods are then compared for their accuracy,
efficiency and reliability.
For the LA, the applicability of post-processing techniques previously used in the ventricles is
explored. The various methods for the LA volume quantification are then described and a novel method is
proposed. The validity and performance of this new method will be analyzed.
Finally, the work will be summarized and future work regarding the application of these
individual anatomical characterizations to quantification of the more comprehensive cardiovascular
system.
3
Chapter 2
Overview of the Cardiovascular System
The cardiovascular system is one of the major systems of the human body. It is responsible for
the transport of oxygen and various nutrients throughout the body via the pumping of blood. This system
consists of the heart and blood vessels.
2.1 The Heart
2.1.1 Cardiac Anatomy
The heart is a hollow, conical, muscular organ approximately the size of a human fist. Weighing
between 250 and 350 grams, it is located in the medial cavity of the thorax between the lungs [1]. It rests
within the pericardium, which is a double walled sac.
The heart itself consists of four chambers: two atria, which receive blood into the heart, and two
ventricles, which discharge the blood as shown in Figure 2.1. It is also separated into two sides, the left
and the right, separated by the septum. Each side consists of a superior atrium and inferior ventricle
separated by a valve. The right side deals with deoxygenated blood; the right atrium (RA) receiving it
from the body and then the right ventricle (RV) pushing it towards the lungs for oxygenation via the
pulmonary valve. The left side deals with oxygenated blood; the left atrium (LA) receives the blood from
the lungs and the left ventricle (LV) expelling it to the rest of the body through the aortic valve. Between
the atria and ventricles lie the atrioventricular (AV) valves. The semilunar valves exist between the
ventricles and the adjacent arteries. The two semilunar valves are the pulmonary valve, between the RV
and pulmonary artery, and the aortic valve, between the LV and aorta.
The cardiac wall itself consists of three layers. The innermost layer, the endocardium, is a thin
membranous lining of the chambers as well as a covering for the fibrous valve skeletons. The
myocardium, the middle layer, is composed of cardiac muscle and is responsible for the contractile
4
motion of the heart. Lastly, the superficial epicardium consists mainly of connective tissue and serves to
protect the underlying cardiac muscle.
Figure 2.1: Anatomy of a Normal Heart [2].
2.1.2 Cardiac Physiology
The heart contracts rhythmically with the resulting impetus pushing blood throughout the
cardiovascular system. A complete contraction and relaxation of the heart is considered one cardiac cycle
and takes approximately 800ms. A heartbeat corresponds to a single cardiac cycle with the average
human adult completing approximately 70 beats per minute [1].
The complete cardiac cycle consists of three phases dictated by the contraction (systole) and
relaxation (diastole) of various anatomies. The first phase, atrial systole, consists of contraction of the
atria. As the AV valves are open and the semilunar valves are closed, this results in blood flowing from
the atria into the ventricles. After this phase, ventricular systole occurs. In this phase the ventricles
contract while the atria relax, resulting in closure of the AV valves whiles the pulmonary and aortic
valves open. This results in blood being expelled from the ventricles into the pulmonary arteries and the
5
aorta. The last phase, isovolumetric relaxation, occurs when there is an overall relaxation of the heart. The
result of this is the closure of the semilunar valves and the filling of the atria with blood from the vena
cava and pulmonary veins [3]. This process is illustrated in Figure 2.2.
This activity is incited by electrical impulses originating in the sinoatrial and AV nodes. Cardiac
muscle has an intrinsic ability to depolarize and contract on its own but the heart is also connected to the
autonomic nervous system which can alter cardiac rhythm.
Figure 2.2: The Cardiac Cycle [4].
2.2 Blood Vessels
2.2.1 Vascular Anatomy
There are three major types of blood vessels in the body. These are arteries, veins, and capillaries.
Arteries carry blood away from the heart while veins carry blood towards the heart. Capillaries are sites
for direct cellular exchange between the blood and the tissues surrounding the capillaries. Almost all of
the arteries carry oxygenated blood and almost all the veins carry deoxygenated blood. The only
exceptions are those of the pulmonary circuit, where the pulmonary artery carries deoxygenated blood
while the pulmonary vein carries oxygenated blood.
6
The major blood vessels have similar wall composition surrounding the blood-filled lumen.
Vessel walls have three distinct layers. The innermost layer, the tunica intima, contains the endothelium
which lines the lumen. The middle layer, the tunica media, is composed of smooth muscle cells and
elastin. This layer is responsible for vasoconstriction, vasodilation, and provides the elasticity
characteristic of the major blood vessels. Finally the tunica externa is the outermost layer and composed
almost entirely of fibrous collagen. It serves to protect, reinforce, and anchor the blood vessels. This
anatomy is shown in Figure 2.3.
Figure 2.3: Blood Vessel Structure [5].
2.2.2 Vascular Physiology
Blood vessels form a closed loop circuit in order to circulate blood throughout the body. These
loops can be considered to begin and end at the heart. The order of blood vessels is always consistent.
Circulation begins from the arteries, which branch into subsequently smaller arterioles, flows through the
capillary beds, and then to small venules which conglomerate into the major veins, thus returning the
blood to the heart.
There are two main circulations when it comes to the circulatory system. These are the systemic
circulation and the pulmonary circulation. The general circulation begins at the LV, which expels
7
oxygenated blood into the aorta. This blood is then carried through the core of the body and extremities,
where it is subsequently deoxygenated and returned to the right atrium via the veins. The pulmonary
circulation begins at the RV. The RV discharges deoxygenated blood into the pulmonary arteries, which
lead to the pulmonary capillaries. The blood is then oxygenated due to action from the lungs, and then
travels through the pulmonary veins into the LA. These circulations can be seen in Figure 2.4.
Figure 2.4: Circulatory System [6].
2.3 Cardiovascular Dysfunction
According to the National Institute of Health (NIH), cardiovascular disease causes approximately
17.5 million deaths each year. This makes it the leading cause of deaths, accounting for over 30% of
deaths worldwide [7]. The term applies to a host of diseases and dysfunctions that involve the heart and
surrounding vasculature. The causes of these may be genetic, environmental, a result of personal habits,
among others.
8
One of the more common cardiovascular issues is heart failure. This is defined by the inability of
the heart to circulate blood effectively. This may be caused by a variety of dysfunctions such as heart
attacks, valve diseases, or hypertension, among others [8].
A common source of cardiovascular dysfunction is arteriosclerosis. This is where the walls of the
arteries become thicker and stiffened, resulting in hypertension. This dysfunction can affect the flow of
blood and thus have a negative impact on the cardiovascular system as a whole [1].
9
Chapter 3
Overview of Cardiovascular Magnetic Resonance Imaging
There are many imaging modalities used to asses cardiac function. These include x-ray, computed
tomography (CT), and positron emission tomography (PET), all of which require ionized electromagnetic
radiation. Modalities that do not require ionized electromagnetic radiation include ultrasound and MRI.
The use of MRI to assess cardiac parameters has become increasingly standard both in research and
clinically. This is because, along with being non-ionizing and non-invasive, it is a very versatile tool that
allows for a much clearer picture of the cardiovascular system. Using the different techniques of cMRI,
we can look at anatomy, measure blood flow, and evaluate tissue motion.
3.1 Fundamentals of Magnetic Resonance Imaging
Magnetic resonance imaging uses the phenomenon of nuclear magnetic resonance (NMR) to
excite protons in hydrogen atoms. Hydrogen is used as is one of the most abundant elements in the human
body, found in both water and fat, and is exceptionally sensitive to magnetic resonance.
When a large, external, uniform magnetic field B0 is applied, the proton spins align along the axis
of the field identified as the z direction. In this case the system is in a state of equilibrium, in which the
net magnetization M0 is aligned with B0 in the z direction. These proton spins precess at a Larmor
frequency ω = γB0, where γ is the gyromagnetic ratio. This ratio has a constant value of 42.58 MHz/Tesla
for protons.
A radio frequency (RF) pulse is applied to create a second magnetic field B1, perpendicular to B0,
and shift the system into an excited state. This adds a transverse element to the net magnetization which
can now be resolved into two components: Mz, the longitudinal component along the original axis, and
Mxy, the transverse component. The properties of the RF pulse determine the amount of magnetization and
the flip angle α. After the pulse is applied, the protons enter the relaxation stage, whereupon they return to
10
the state of equilibrium. As a proton precesses around B0, the rotation of the transverse signal produces a
measurable current in a proximal RF coil. This process is illustrated in Figure 3.1.
There are two types of relaxation: spin-spin relaxation, which corresponds to the decay of Mxy,
and spin-lattice relaxation, which corresponds to the recovery of Mz. Their respective time constants are
T1 and T2. Different tissues have different time constants, thus allowing for a source of contrast in MR
images.
A particular slice selection is imaged through use of the basic principles NMR. A gradient field is
applied in the z direction so that only a particular slice will be exposed to the resonant frequency and will
experience excitation. Spatial localization is done through two mechanisms: phase encoding and
frequency encoding. Phase encoding occurs when a gradient magnetic field is applied to the y direction.
This causes a dephasing of the voxels in the y direction. Meanwhile all the voxels along a particular row
in the x direction will retain the same relative phase. Frequency encoding is applied afterwards where a
gradient is applied along the x direction, also known as the readout direction. This causes the precession
frequencies to vary along the readout direction.
This data obtained after these sequences are interpreted as scans of Fourier space. Using an
inverse Fourier transform, a 2D image can be reconstructed.
Figure 3.1: Precession of a proton back to equilibrium position after application of B1 [9].
11
3.2 Cardiac Magnetic Resonance Imaging
Cardiac MRI (cMRI) is achieved using a specialized cardiac coil in conjunction with the larger
MRI machine. This coil, akin to a chest pad, is placed around the thoracic cavity and allows for more
focused imagining of the heart and surrounding vessels. Cardiac imaging can difficult due to the constant
motion of the heart. As images are captured over one or more cardiac cycles, artifacts are introduced as a
result of both tissue and blood movement. In order to minimize movement, patients are commonly asked
to hold their breath for up to 20 seconds after exhaling completely in order avoid respiratory artifacts and
to keep the heart in a consistent location for imaging.
Using cMRI, we can obtain a large variety of data that pertains to both the structure and function
of the cardiovascular system. The particular data acquired varies depending on the imaging protocol used
during the MRI. The three most commonly used protocols are cine, tagged, and phase contrast (PC) MRI.
3.2.1 Cine Cardiac MRI
The most used protocol for cardiac imaging is cine cMRI. This protocol uses the basic techniques
of MRI explained above in order to obtain images of the heart. The majority of the images fall along two
major axes. These are the long axis, which extends lengthwise from the apex to the base of the heart, and
the short axis (SA), which is perpendicular to the long-axis and roughly perpendicular to the valve plane.
Cardiac MRI allows for great versatility in imaging, allowing an operator to obtain a variety of view of
the heart, both along the major axes and in oblique planes. The most common studies involve a series of
SA image slices along the length of the heart as well as two-chamber (2ch) and four-chamber (4ch) views
obtained through radial slicing along the long axis. Figure 3.2 below illustrates this process.
Cine cMRI has many advantages as it allows the imaging of a slice throughout the entire cardiac
cycle. This allows a qualitative view of the heart in order to observe any dysfunction. Post-processing of
the images also allow quantitative data to be obtained. As dimensions for the image are known through
scanner properties, values such as wall thickness and encompassed blood volume can be obtained over the
12
entire cardiac cycle for each image. This data can be compiled and used to provide a quantitative
perspective of cardiac function.
Figure 3.2: Slice prescriptions for cMRI. The images on the left show the prescribed slices represented by the bold lines. The corresponding cMRI images are displayed on the right [10].
13
3.2.2 Tagged Cardiac MRI
Tagged cMRI is a protocol used almost exclusively by the research community due to its post-
process heavy nature [11]. While there is lower tissue contrast, tagged cMRI allows for accurate
observation of tissue motion.
In tagged cMRI, gridlines are imposed on the underlying myocardial tissue, as shown by Figure
3.3. This is done using a technique known as spatial modulation of magnetization (SPAMM). In this
technique, RF pre-pulses are used to cause saturation in the tissue. These patterns of saturation are
oriented perpendicular to the image plane. As the cardiac wall deforms as a result of contractile motion,
the tags can be seen to deform correspondingly. Due to T1 relaxation, the tag lines fade over the course of
the cardiac cycle. As a result, the tags become harder to distinguish in the latter parts of diastole.
Processing of tagged imaging can allow motion to be tracked throughout the cardiac cycle. This
allows for derivation of quantitative parameters that relate to the functional nature of the myocardial
tissue such as shear, torsion, and rotation.
Figure 3.3: Cine and corresponding tagged MR images at ED (a) and ES (b) [12].
14
3.2.3 Phase Contrast Cardiac MRI
PC cMRI differs from both cine and tagged cMRI in that it looks at the flow profile of blood in
the cardiovascular system as opposed to solely the structure of the anatomy.
Phase images are obtained using the process of velocity encoding [11]. A flow encoding gradient
is used in order to create images that are essentially velocity maps. Protons moving at a constant velocity
will undergo a phase shift proportional to the velocity when they are exposed to the gradient. The images
are black and white with flow in a particular direction shown in white and the reverse flow shown in
black. Stationary tissue is seen as being grey. The intensity of the color corresponds to the velocity and
the MRI operator can set a maximum intensity at a particular velocity. Sequences can be made to measure
in-plane or through-plane motion. The images obtained can be seen in Figure 3.4.
Obtaining a velocity profile for the cardiovascular system allows data to be gathered regarding
flow parameters such as speed and volume. These can be used to further extrapolate more parameters and
used in conjunction with other cMRI protocols to obtain data regarding to overall cardiovascular function.
Figure 3.4: Output of PC MRI of transected aorta. Magnitude (a) and corresponding phase (b) images.
15
Chapter 4
Pulse Wave Velocity and the Quantification of Arterial Flow
Blood flow in the arteries is greatly impacted by various cardiovascular events and dysfunction.
As such it is important to find an effective and reliable method to quantify blood flow and calculate any
changes that occur. The majority of analysis techniques use the time domain to calculate the transit time
of blood flow. In this section, a frequency domain approach to this analysis is considered and evaluated.
The work in this chapter has been accepted as an abstract in the 20th annual meeting for the International
Society of Magnetic Resonance in Medicine [13].
4.1 Arterial Flow and Pulse Wave Velocity
4.1.1 Overview of Arterial Flow
Arteries are not just passive conduits through which blood flows. Instead, they constitute a system
that regulates pressure, flow, and cardiovascular function. This regulation occurs as a result of arterial
capacitance and resistance, which are derived from the structure and quantity of elastin, collagen, and
smooth muscle [14]. For an overview of arterial anatomy, refer to Section 2.2.1.
Large arteries such as the aorta can store approximately 50% of the stroke volume during systolic
contraction [15]. During diastole, the recoil as a result of elasticity helps drives a continuous blood flow
during the diastolic portions of the cardiac cycle. Transmission line models have been proposed, using the
electrical transmission line as an analogue to arterial flow [16]. This model is illustrated in Figure 4.1.
The elastic characteristic of an artery is affected by its inherent stiffness. This stiffness impairs
the ability for an artery to expand and contract and thus impairs the conversion of pulsatile motion into
continuous blood flow. This stiffness is quantified using a measure called pulse wave velocity through a
process discussed further in this chapter.
16
Figure 4.1: Transmission line model for systemic circulation. R is resistance, C is capacitance, L is inductance, and G is the leakage (conductance) [16].
4.1.2 Significance of Pulse Wave Velocity
Pulse wave velocity is a measure of arterial stiffness. It is related to the incremental elastic
modulus, Einc, via the Mons-Korteweg equation stated as
∙2
4.1
where h is the vessel wall thickness, r is the vessel radius, and ρ is blood density which has the value
1060 kg/m3 [14]. Using this equation, Bramwell and Hill were able to derive a model relating PWV with
distensibility through
1
∙ 4.2
with the assumption that the vessel is compliant and contains incompressible nonviscous liquid [17]. The
calculated distensibility can be further used to find strain using
∆
∆∙ ∆
4.3
where ∆P is central pulse pressure, A is area of vessel, and ∆A = (Amax - Amin)/Amin [18].
Stiffness is when the distensibility of the arteries decreases thus affecting blood flow. This results
in an increase of pressure due to the decreased capacitive effect of the arteries with diminished elasticity.
Subsequently, there is an increase in left ventricular properties such as load and mass [19]. There is also
17
an increase in pressure wave reflection resulting in an increase in systolic pressure, further increasing
ventricular load. These changes in the cardiovascular system lead to various dysfunctions.
The increase of stiffness in large arteries can be correlated to a variety of cardiovascular
dysfunction and mortality. This is especially true in cases of pre-existing conditions. In diabetic patients,
there is a direct correlation between arterial stiffness and cardiovascular mortality [20]. Hypertensive
patients have also been found to have an increased PWV that could be directly associated with higher
cardiovascular risk [21]. This was corroborated by a large study of hypertensive subjects (n = 1980),
which showed an association between arterial stiffness and both cardiovascular and general mortality
[22]. Studies of renal disease in patients have also shown that cardiovascular events and mortality
correlated with a marked increase in arterial stiffness measured using PWV [23].
The significance of PWV as a measure extends further from sufferers of disease into the general
population. A large study (n=2835) showed that in seemingly healthy individuals, stiffness in the arteries
is a predictor of cardiovascular dysfunctions such as coronary heart disease [24]. Arterial stiffness as
measured by PWV is a risk factor of various cardiovascular issues such as atherosclerosis [25], coronary
heart disease [26], hypertension [27], and stroke [28]. In the geriatric population, arterial stiffness was
shown to be an indicator or cardiovascular and general mortality [29].
Such findings have highlighted the importance of pulse wave velocity in both clinical and
research settings. The information obtained through PWV can be used to evaluate the cardiovascular
health of patients as well seeing the affects that various dysfunctions have on the arteries. This is further
evidenced by the use of PWV in the guidelines for hypertension treatment by the European Society of
Hypertension [30].
18
4.1.3 Calculation of Pulse Wave Velocity
Pulse wave velocity must be calculated and is not obtained from a direct body measurement. It is,
in fact, done in two stages: the acquisition stage where the waveform data is collected, and the evaluation
stage where the PWV is calculated.
The acquisition of pulse wave data must be done at two points in order evaluate the movement of
the wave. This can be done in a variety of ways. The most reliable method is that of cardiac
catheterization. This is the most effective method because it provides the most accurate waveform data
with high temporal resolution. However, due to its invasive nature, it is not an ideal method to obtain the
pulse waveform. Therefore noninvasive methods have been sought in order to obtain the velocity profile.
Of these techniques, cMRI is the most effective as it provides a highly resolved image with relatively
little noise. The images are obtained using the PC MRI procedure outlined in Section 3.2.3.
The calculation of PWV is no different from any other velocity calculation and is done through
the simple formula
4.4
where Δd is the distance between the two measurement points and Δt, known as the transit time, is the
time required for the pulse wave to travel. Finding the distance is relatively facile and while specifics
depend on the method used to acquire the data, it is essentially just a calculation of distance between the
physical data acquisition points. This process involves contouring images using post-processing software
and will be further explained in Section 4.2. It is the calculation of transit time that becomes difficult.
There are various methods to calculate transit time for cMRI. The majority of these require finding the
corresponding points in the two measured waveforms. The time difference between the two points is then
used to find the transit time. These methods will be further discussed in Section 4.3. A frequency-based
approach to calculate transit time will also be introduced in Section 4.4. The efficacy of these approaches
will be further explored throughout this chapter.
19
4.2 Contouring Cardiac Flow Images and Distance Calculation
The post-processing of the images is done through both commercially available software CAAS
MR Flow (Pie Medical Imaging, Maastricht, The Netherlands) and custom designed in-house software.
However, before data can be obtained, certain regions of interest (ROI) must first be defined. This is
because the actual vessels are only a portion of the actual image. Therefore, in order for accurate
quantification to occur, the bounds of what the post-processing software will consider relevant have to be
set. For blood vessels this is done by the user identifying the vessel in question and edge detection
algorithms in the CAAS software defining its inner walls. There is some room for error and as such, the
user must manually check that the contours correctly define the vessel. The process is simplified by the
fact that, barring a small change in area due to distension, the blood vessels remain a relatively constant
circular shape throughout the cardiac cycle. This is all done on the magnitude image, as it provides a
clearer picture of the anatomy, and is then transferred to the corresponding phase images. This allows the
software to determine flow velocities from the phase images only within the defined area. This process is
shown below in Figure 4.2.
Figure 4.2: Image of contouring the ascending (red) and descending (green) aorta using CAAS MR Flow. The contours are copied to the phase image. In this case the automatic contour for the descending aorta would have to be corrected manually.
20
In order to find the distance needed in the PWV calculation (Equation 4.4), the images must be
further contoured. This is done by using the reference image. This is the image that was used during the
MRI scan in order to select the particular slices for the PC MRI. A user can see the slice projections on
the reference image, and use that to draw a contour between two of the relevant projections. The software
uses this contour to calculate the distance between the points where blood flow was measure. This is
illustrated in Figure 4.3.
Figure 4.3: Reference image showing slice projections (a) and subsequent contour (b) used to find distance between ascending and descending aorta flow points. Note the contour is drawn to run along the midline of the vessel.
4.3 Common Methods for Transit Time Determination
There are a few commonly applied methods to calculate the transit time for PWV. These methods
consist almost exclusively of comparing corresponding landmarks at the two flow measurement points in
the time domain.
Although the magnitude of the waveform changes as blood flows through the systemic circuit,
there is a characteristic shape which allows for determination of distinct landmarks. This waveform
change occurs in both normal and dysfunctional cardiovascular systems. The waveform changes can
occur due to geometry, such as the curve of the aortic arch which results in impedance changes and
21
reflected waves, and changes in pressure and flow due to shunting of blood through the branches such as
with the carotid and subclavian arteries. It is important to note that this may also introduce noise which
can cause difficulties in analysis.
The methods for flow analysis using these landmarks can be seen used for papers in various
cardiovascular publications. The majority of these are techniques used originally with ultrasound and
catheterization data, which have been subsequently adopted for cMRI use. These include peak analysis,
interpolated curves, and onset time analysis.
4.3.1 Peak Analysis Using a Quadratic Fit
In quadratic peak analysis, transit time determination is done by comparing the maximums of
both measured flows. However, due to the resolution, data may not include the absolute maximum of the
flow. Therefore a quadratic is fit to the maximal area and the absolute maximum is determined by that
quadratic. By fitting a quadratic to this part of the waveform, the point where flow is at a maximum can
be interpolated and its corresponding time can be found. When this is done to both the waveforms, the
difference in the two time points can be used to calculate transit time.
This analysis technique was applied using both three points and five points in order to fit a
quadratic to the maximal area. This is showing in Figure 4.4. This served as a cursory qualitative check
on the applicability of the quadratic function to interpolate the point of maximum flow. While not ideal,
the resolution of the data should mean that the shape of the quadratic should not undergo any drastic
changes when taking into account five points versus three. Therefore there should not be a drastic change
between the transit times calculated by the two methods. If there is a large change in a significant number
of studies, it will indicate that a quadratic fit may not accurately represent the shape of the maximal areas
in the flow data.
The specific methodology for quadratic fitting is fairly simple. First, the maximal point of the
waveform is found. Due to the resolution of PC MRI, this may not represent the true maximum but it will
be the closest point to it. Then points from either side of this point are used to create the quadratic. For a
22
three point quadratic fit, one point on either side is sampled. For a five point fit, two points on either side
are used. Using analysis software a quadratic function is realized using these points. Due to the nature of
flow waveforms, the quadratic will always be negative, characterized by a downward concavity.
Therefore the maximal point will always be the vertex of the function, which in turn provides the relevant
time point. This process is repeated for the second waveform. From there, the transit time can be easily
calculated as the difference between the two maximal times. This can be applied to Equation 4.4 to find
the PWV.
(a)
(b) Figure 4.4: Peak analysis using three-point (a) and five-point (b) quadratic fits
0 100 200 300 400 500 600 700 800 900 1000-50
0
50
100
150
200
250
Time (ms)
Flo
w (
ml/
s)
Asc Aorta DataAsc Aorta Peak QuadraticDescAorta DataDescAorta Peak QuadraticAsc Aorta MaximumDesc Aorta Maximum
Transit Time = 42.05ms
0 100 200 300 400 500 600 700 800 900 1000-50
0
50
100
150
200
250
Flo
w (
ml/
s)
Time (ms)
Asc Aorta DataAsc Aorta Peak QuadraticDesc Aorta DataDesc Aorta Peak QuadraticAsc Aorta MaximumDesc Aorta Maximum
Transit Time = 48.10ms
23
4.3.2 Cubic Spline Interpolation of PC MRI Waveforms
Another method to aid in transit time determination is to interpolate more points from the PC
MRI data obtained. This allows for more data points to be used as landmarks for comparison between the
two waveforms. However, interpolating the data using polynomial parametric curves does not provide
data in regards to the behavior of blood in the arteries. This is because data points that are further away
still have a large impact on the interpolated curve. Therefore Bezier cubic splines are used to interpolate
the data instead, as seen in Figure 4.5 below.
Figure 4.5: Polynomial (a) and spline (b) interpolation of an identical data set [31]. Note the spline interpolation seems more true to the original data points.
In fact, cubic spline interpolation is one of the more common methods to achieve an increase in
data points. In this method, cubic polynomial curves are constructed between every two data points in the
original set. These curves are combined to create a piecewise function with a continuous second
derivative. This allows for minimization of undue influence from distant points and thus creates a fit that
is more true to the original data. Most analysis software and coding platforms already contain functions
that can interpolate the data. The output of this interpolation is displayed in Figure 4.6. From this point,
various landmarks can be selected and compared such as methods similar to the peak analysis in Section
4.3.1 or the commonly used onset time analysis discussed in Section 4.3.2.
24
Figure 4.6: Spline interpolation of PC MRI data from ascending and descending aorta.
4.3.3 Onset Time Analysis
Transit time determination can also be done through onset time analysis. For onset time analysis,
the landmark for comparison is set as a point at which the vascular flow reaches a certain percentage of
the maximum flow at each of the measurement points. The difference between the times at which this
point is reached on the respective curves is found as the transit time. Methods using values between and
including 10 - 20% of the maximum flow can be found in various literature. The reasoning behind this
method is that is minimizes the discrepancy caused by using a single peak point. However, this method
requires some form of interpolation in order to provide points that will be close to the target value. Spline
interpolation is commonly used for this. This method is demonstrated on Figure 4.7 below.
Occasionally there may be issues regarding the offset of the flow curves as data points may
actually have a negative value. This is because, during the actual scan itself, flow values can be offset
either positively or negatively based on backflow in the artery at time of measurement. Phase errors
during PC MRI can also offset the flow, requiring correction. These errors can arise from setting an
encoding velocity, during the scan, that is lower than the peak velocity which results in aliasing, or
velocity wraparound. Deviation of the image plane due to motion, inadequate spatial resolution, and field
0 200 400 600 800 10000
50
100
150
200
250
300
350
Time (ms)
Flo
w (
ml/
s)
Interpolated Asc AortaOriginal Asc Aorta DataInterpolated Desc AortaOriginal Desc Aorta Data
25
inhomogeneity can also distort flow data [32]. The majority of analysis software allows for correction of
this offset by the identification of systole and the shifting of all points based on these points.
Figure 4.7: Onset time analysis using landmark at 15% of maximum flow
4.3.4 Peak Acceleration Analysis
In peak acceleration analysis, the landmark used for comparison is the point at which the rate of
flow is at its maximum value. The rate of flow will be at a maximum as the LV is contracting and
therefore imparting the largest amount of impulse upon the blood during the cardiac cycle. In order to find
this point, the derivative of the flow data must be taken in order to obtain the rate of flow over time. From
this new data set, the maximum point is then located for both of the measurement points. The difference
in times at which the maximum rates occur is taken as the transit time for PWV calculation. This process
is illustrated in Figure 4.8.
26
0 100 200 300 400 500 600 700 800 900 1000-50
0
50
100
150
200
Time (ms)
Flo
w (
ml/
s)
Ascending Aorta DataDescending Aorta Data
0 100 200 300 400 500 600 700 800 900 1000-1.5
-1
-0.5
0
0.5
1
1.5
2
Time (ms)
Flo
w R
ate
(Flo
w/s
)
Ascending Aorta Flow RateDescending Aorta Flow RateAscending Aorta Maximum RateDescending Aorta Maximum Rate
Transit Time = 31ms
(a)
(b) Figure 4.8: Plots of analysis using the peak acceleration method. Plot (a) is the flow data while plot (b) shows the rate of flow for both measurement points.
4.3.5 Issues with Transit Time Determination in the Time Domain
Though these methods are commonly implemented, there are flaws regarding their reliability.
These issues stem mainly from the fact that the techniques are adopted from their use with earlier
methods such as cardiac catheterization. While the methods are still reasonably viable, the differing
nature of MRI and the data it produces causes some problems.
A major issue with PC MRI data is the significantly reduced temporal resolution. This is because
the PC MR images require two separate acquisitions with different flow-encoding gradients in order to
correct any phase errors. As a result, an image is collected approximately every 30ms. Therefore, in a
complete cardiac cycle, approximately 32 data points will be collected. Of these data points, roughly 10
will fall into the pulse wave that exists during systole and be significant in time domain-based analyses.
27
Any deviation in the quantification of even a single one of the significant points, whether by user error in
contouring or due to poor image data, will result in a large error in the calculated transit time and
therefore the overall PWV.
On the other hand, catheterization data can have about an order of magnitude higher temporal
resolution than that of PC MRI. This can be seen in Figure 4.9. This results in a lessened influence of a
single data point on the overall quantification of the flow, allowing for a more precise and accurate
quantification. This resolution, combined with its reduced noise and artifacts, is one of the reasons that
results from catheterization data are held as gold standard.
(a)
(b) Figure 4.9: Comparison of a 300ms portion of data from catheterization (a) and PC MRI (b). The
temporal resolution from catheterization data is 4ms while that from PC MRI is 29ms.
0 50 100 150 200 250 30092
93
94
95
96
97
98
99
100
101
Time (ms)
Pre
ssur
e (m
mH
g)
0 50 100 150 200 250 300 3500
50
100
150
200
250
300
350
Time (ms)
Flo
w (
m/s
)
28
The impetus, then, is to find a method that would allow for both more precision and increased
accuracy in PWV quantification using PC MRI. This would be done either through increasing the
temporal resolution of the scanner output or to find a calculation method that reduces the impact that error
in a single data point can cause. An alternative calculation method will be discussed in Section 4.4.
4.4 Alternative Method for Transit Time Determination Using the Frequency Domain
It was previously asserted that a major issue with the use of PC MRI data in PWV calculations is
the relatively low temporal resolution. A method is proposed where data is first converted from the time
domain to the frequency domain before calculating the transit time. This method is similar to one
proposed in 1988 by Latson et al. for use with catheterization data [33]. By transferring the data into the
frequency domain, all the obtained data points are taken into account, which in turn minimizes the error
that can be caused due to a single data point.
This method requires taking the flow profiles of the two points along the artery, vproximal and vdistal,
and using a Fourier transform to convert them into the frequency domain.
Ƒ v V ω 4.5
Ƒ v V ω 4.6
From here, a transform function, H, can be expressed as the quotient of the two Fourier transforms:
ωV ω
V ω 4.7
The pulse is assumed to maintain a constant shape as it travels throughout the body. As such, one
can assumed a minimized change in the shape of the waveform, allowing the distal point to be expressed
as time shifted version of the more promixal point:
V ω A ∙ V ω ∙ π (4.8)
where A is a scale factor. This allows us to substitute this expression for the distal point into Equation 4.7
for the transfer function:
ω A ∙ π (4.9)
29
Finding the linear phase characteristic of the transfer produces:
∠ ω 2π 4.10
The slope of the linear phase characteristic is 2π , where is the transit time between the
proximal and distal point. This can then be used to find the value for PWV.
Using this method, the effect of error due to a single point is minimized. Even if there is a change
in shape of the waveform between the proximal and distal points of measurement, linear phase
characteristic of the transfer function will still remain relatively linear at the lower frequencies as shown
in Figure 4.10. This will still allow for accuracy in transit time determination, allowing for a more true
determination of PWV.
(a)
(b)
Figure 4.10: Plots of linear phase characteristics used for transit time determination. Plots are included with both a minimal change in waveform shape (a) and a large change in shape (b) between the proximal and distal measurement points.
30
4.5 Comparison of Quantification Methods in Pulse Wave Velocity Calculation
In order to test the validity of the frequency domain approach to transit time determination, PWV
calculations were made using the proposed approach and compared to results from point-to-point time
domain methods. The subject pool used contained both normal cohorts as well as patients diagnosed with
pulmonary hypertension. Subjects with this pathology are known to have an increase in stiffness of the
pulmonary arteries. In this validation, there was no gold standard velocity data as catheterization was not
performed in relation to this study. Instead, the true velocity is not certain but the differences between the
normal and hypertensive hearts was used for validation.
4.5.1 Methodology
The study was conducted (n = 12) using four normal subjects and eight patients with pulmonary
hypertension. The subjects underwent cMRI and PC MRI data was acquired from the main pulmonary
artery (MPA), proximal to the pulmonary valve, and in the right pulmonary artery (RPA). The studies
were conducted with institutional review board (IRB) approval from both Auburn University and the
University of Alabama at Birmingham School of Medicine.
The MRI was performed on a 1.5T MRI scanner (CV/i, GE Healthcare, Milwaukee, WI)
optimized for cardiac imaging. Free breathing non-segmented cine PC gradient echo was used in order to
obtain the necessary flow images of the MPA and RPA cross sections. The parameters of the scan were: a
6mm slice thickness, 32 phases, a 150-200cm/s encoding velocity, field-of-view of 32 x 40cm, scan
matrix of 256 x 128, 20° flip angle, NEX of 2-3, 18ms TR, and 5.4ms TE.
After the images were acquired, they were contoured using CAAS MRV software with the
method described in Section 4.2. The users manually defined the ROI's as the cross sections of the MPA
and RPA. The data was then sent to custom in-house software, where the transit time was determined by
both the frequency domain technique as well as point-to-point time domain methods. The specific time
domain methods used were onset times at 10%, 20%, 30%, 40%, and 50% onset as well as peak velocity
31
and peak velocity rate methods. These transit times were then used to calculate PWV in order to get a
measure of the arterial stiffness in the pulmonary arteries.
4.5.2 Results
The calculated PWVs using transit time determination in the time domain as well as those
calculated by the frequency domain method are shown below in Table 4.1.
The results show that there is a large amount of variation between the various time domain based
methods for each patient group. The standard error is also considerably larger in the time domain based
methods than it is in the frequency domain methods. Also, the difference between the two patient groups
did not reach statistical significance when using the time domain methods whereas they were significantly
different with the use of the frequency domain methods in calculating transit time.
Table 4.1: PWV (Mean ± Standard Error) measured in m/s from PC-MRI data acquired in the MPA and RPA
Normal
Pulmonary Hypertension
P vs Normal
10% -29.6 ± 65.9 3.4 ± 1.6 0.031
20% 19.3 ± 32.5 4.2 ± 1.7 0.168
30% 4.3 ± 6.1 6.2 ± 2.9 0.102
40% 6.4 ± 3.2 7.1 ± 3.4 0.218
50% 6.3 ± 3.4 6.2 ± 3.5 0.0928
Peak 6.9 ± 2.9 7.8 ± 3.9 0.317
Peak Accel 11.6 ± 26.5 7.5 ± 4.6 0.0883
Freq 4.5 ± 1.3 6.3 ± 1.1 0.0401
32
4.5.3 Discussion
In this section, we attempt to highlight the issues with the time domain methods for PWV
calculation and show the efficacy of using a frequency domain based approach.
The large variation between the various time-domain methods is indicative of the problem caused
by the low temporal resolution of PC MRI. This is further supported by the large amount of standard error
seen in some of the specific time domain based methods such as the 10% and 20% onset time approaches.
This also raises the concern of standardization in time-domain based PWV calculations, as the use of a
different method results in a largely different result. Finally, the lack of significant difference between the
normal subjects and pulmonary hypertensives, a group known to have stiffer arteries, highlights the issue
of using such methods for various pathologies.
On the other hand, the frequency-domain method showed a robustness in the face of changes in
flow waveform shape as it flows down the artery. This is due to the lessened impact of single data points
on the overall calculation of the transit time. Also, the significant difference between the PWV of the
pathology from the normal suggests that this approach can be effectively used to quantify the changes that
occur in the PWV due to various cardiovascular dysfunctions.
4.5.4 Conclusion
The frequency-domain method is a reliable and effective method to calculate PWV. It has been
shown to hold various advantages over time-domain methods as a result of its reduced susceptibility to
changes as a result of errors from a single data point. The use of the entire waveform also allows for more
precise measurements within a subject group as well granting the ability to differentiate the affects of
various pathologies on arterial pulse wave velocity.
33
4.6 Further Work
Whilst the frequency domain method has been compared to the time domain based methods, it is
also important to validate the method against a gold standard. In these studies, invasive data was not
available. In order to evaluate accuracy of noninvasive determination of PWV through PC MRI and the
frequency-domain method, invasive data would need to be collected alongside MRI images. The invasive
data would provide a gold standard, showing the actual PWV in the artery, and the noninvasive
calculation would be checked for accuracy in determining the true value for PWV.
More work should also be done in regards to a variety of approaches in the frequency domain.
While the use of the Fourier transform has shown to be effective in regards to reducing issues caused by
the low spatial resolution, other transforms and multipliers could be experimented with to see whether
error could be further reduced and a more accurate determination achieved.
34
Chapter 5
Quantification of the Left Atrium
Knowledge regarding the left atrium has grown considerably since the advent of noninvasive
imaging modalities. The LA has been shown to remodel and change due to various pathologies and
cardiovascular events. Therefore, it is important to find an effective method to quantify the atrium. The
work in this chapter regarding the quantification method for the LA has been accepted as an abstract in
the 21st annual meeting for the International Society of Magnetic Resonance in Medicine [34].
5.1 Overview of the Left Atrium
The left atrium (LA), while originally viewed as a passive transport channel between pulmonary
veins and the LV, has become increasingly relevant clinically for the prediction and evaluation of
cardiovascular disease. This has become all the more so as new technologies and techniques allow for
evaluation and quantification of the LA in vivo.
Anatomically, the LA is located superior to the LV, connected by the atrioventricular junction. As
explained in Section 2.1.1, it receives blood from the lungs before transferring it to the LV. Unlike the
LV, which is more uniform along the short-axis, the LA has a more windsock like shape as can be seen in
Figure 5.1. Blood flow between the two chambers is partially regulated by the mitral valve (MV). The LA
is defined by smooth muscular walls that vary in thickness based on the specific wall in question. For
example the superior wall can be thicker than the lateral and anterior walls by over 1.5mm [35].
35
` (a) (b)
Figure 5.1: 3D models of LA (a) and LV (b) created using Matlab with contoured 3T cine MRI images.
LA function during the cardiac cycle can be broken down into three main phases, diagrammed in
Figure 5.2 below. The first phase, the reservoir phase, corresponds with LV systole and isovolumic
relaxation. During this, the LA receives and stores the pulmonary venous return. During the next phase,
the LA acts like a conduit and passively transfers blood to the LV. This behavior occurs during early
diastole and is theorized to be related to LV suction. In the final phase, corresponding with the final phase
of diastole, the LA actively contracts and pumps blood into the LV [36]. This transfer account for
approximately 15-30% of the LV stroke volume [37].
Figure 5.2: LA pressure-volume loop showing the three phases of atrial action during the cardiac cycle [36].
36
Due to the directly interactive and dynamic relationship between the LA and LV, quantification
of the LA allows for clinical evaluation of LV condition. A change in LV stroke volume directly affects
both the active and passive emptying volumes of the LA [38]. Also, there is a marked increase in atrial
contraction in response to stiffening of the LV. This is further evidenced in studies of heart physiology in
response to aging.
As well as allowing clinicians to gain information about the LV, quantification of the LA can
help reveal overall cardiovascular health. The majority of atrium related dysfunction originates from the
stress and tension of the atrial walls during ejection. However, LA preload, which is volume dependent
also plays a role. As there is increased dilation of the LA, the muscle fibers stretch. While these fibers are
resilient, some of this stretching becomes permanent. As this is a progressive process, a threshold fiber
length can be reached, leading to a decline in shortening and contractility of the LA [39,40]. An indicator
of this is atrial volume. Increase in LA volume has been associated with dysfunctions such as stroke [41],
congestive heart failure [42], MV disease [43], aortic stenosis [44], and atrial fibrillation [45]. There has
also been evidence linking and increase LA volume with aging in terms of general cardiovascular
morbidity and mortality [46]. This makes the accurate quantification of LA volume increasingly
important both clinically and in research.
5.2 Contour Propagation for the Left Atrium
Whilst the imaging protocol for the LA follows a standard cine MRI method, issues do arise
when it comes to processing and contouring the images. Drawing contours onto every timeframe is
tedious and highly time consuming. As such, methods for propagating contours drawn onto a single
timeframe across the entire cardiac cycle were developed. These methods were developed primarily for
the ventricles of the heart, primarily the LV. In order to appropriately quantify the LA, its unorthodox
geometry, relatively thin walls, mitral annular motion, the presence of pulmonic veins, and the atrial
appendage must be taken into account. However these considerations cast doubt onto the efficacy of
contour propagation for the LA. Propagation is further made difficult because of the prevalence of flow
37
artifacts in MRI images of the LA due to its proximity to various blood vessels. In this section, the
applicability of a dual contour propagation method is examined.
5.2.1 Dual Contour Propagation
In contour propagation, a manually defined contour in a specific timeframe is used to create
contours for images along the entire cardiac cycle. In 2009, Wei Feng proposed a geometry independent
semi-automated dual-contour propagation that can be applied to both ventricles of the heart [12,47]. This
method utilizes contours drawn on both the ES and ED timeframes and propagates them using non-rigid
registration (NRR).
In NRR, a template image is used in order to create contours onto a source image through the use
of a deformation field. The deformation is computed as the field required to warp the source image to fit
onto the template image. The template image will always contain contours either manually drawn or from
a previous propagation. The calculated field is then applied to the contours on the template image in order
to produce corresponding contours for the source image.
With the dual-contour propagation method, contours drawn on the ES and ED timeframe images
are propagated independently via NRR as illustrated in Figure 5.3. The contour from the ED timeframe is
propagated forward through systole and backward through diastole up to but not including the ES
timeframe. The contours from the ES timeframe are propagated in the same manner, again up to but not
including the ED timeframe. These two independent sets of contours are then combined into a single B-
spline contour through a weighted least-squares fit. The weight of each set of contours in a specific
timeframe is determined by the separation from the manually drawn contour. For a timeframe closer to
ES, the weight will be towards the contour propagated from the ES manual contour and less from that
propagated from the ED manual contour. This will be reversed for timeframes closer to ED.
38
Figure 5.3: Propagation for LA 4ch view as determined by dual-propagation method.
5.2.2 Method
To validate the application of the dual-contour propagation method, 10 normal volunteers
underwent cMRI. IRB approval was obtained from Auburn University to conduct the study. The subjects
were between the ages of 19 and 52, and presented with no cardiac dysfunction. In order to test
repeatability, two sets of images were taken, the second between one and four weeks after the initial
cardiac scan. Images were taken in the 2ch, 4ch, and SA views taken from the LA apex to a point past the
mitral annulus.
The MRIs were performed on a Siemens Verio 3T MRI scanner (Siemens, Erlangen, Germany).
A retrospectively-gated breath-hold balanced SSFP sequence was used. The parameters of the scan were:
an 8mm slice thickness, field-of-view of 36 x 40cm, a scan matrix 258 x 128, 40° flip angle, 5,4ms TR,
and 1.4ms TE.
39
The images were then contoured using custom in-house software. Contours were drawn on the
ED and ES timeframes on all the SA slices as well as on the 2ch and 4ch views. The atrial appendage and
pulmonic veins were excluded from the contours based on the adjacent atrial segments. These contours
were then propagated using the dual-contour propagation method described in Section 5.2.1. Landmarks
were also places on the mitral annulus in order to account for annular motion in calculation.
The contours were then used to calculate LA volume-time curves (VTC) using two separate,
already validated methods: the serial short-axis (SSA) method and the area-length (AL) method. These
methods are both explained in Section 5.3. The resulting data was then statistically analyzed in order to
evaluate validity of the propagated contours. Differences at each timeframe during the cardiac cycle were
computed for each method between the two scan times for each of the two methods. Mixed modeling with
compound symmetry covariance structure applied to the differences was used for the analysis.
5.2.3 Results
The VTCs were computed for both the SSA and AL methods averaged over the study population
for each scan. These are shown in Figure 5.4 below.
(a) (b)
Figure 5.4: Left atrial volume-time curves averaged over 10 normal subjects computed using the serial short-axis (a) and the area-length (b) methods using two different scans (Scan 1 and Scan 2).
40
Table 5.1 below shows the least-squares estimate of the mean differences between the two scans
for each method. Along with the VTCs, atrial volume, ejection fraction, and rates of filling and ejection
were also computed in all the scans using both the SSA and AL methods. There were no significant
differences between the two scan times for any of these values. Also, the values were all found to be
within an acceptable range for the LA.
Table 5.1: Least-squares estimates of the mean difference in LA volume-time curves between Scan 1 and Scan 2.
Method Estimate Standard
Error DF t Value Pr > |t| Alpha Lower Upper
AL 7.3 3.8 16 1.93 0.07 0.05 -0.72 15.4 SSA 5.7 3.8 16 1.51 0.15 0.05 -2.3 13. 8
5.2.4 Discussion
From the results, it can be seen that the dual-contour propagation method can, in fact, accurately
be used for the determination of VTCs using both the SSA and AL methods. The results also showed the
repeatability when the contouring method was applied for two different scan points. As the methodology
called for landmarks placed at the mitral annulus, the VTCs were unaffected by mitral annular motion that
would otherwise create difficulties from contours of the LA near the atrioventricular junction. The use of
the dual-propagation method is effective in producing LA contours. The fact that manual input is reduced
to contouring only the ED and ES timeframes greatly reduces the time spent in post-processing of the
cMRI images.
41
5.3 Accepted Methods for Left Atrial Quantification
Due to its ubiquity, the current gold standard for LA quantification is through the use of an
echocardiogram [48]. However, cMRI, providing an increased resolution and temporal clarity, has the
potential to provide much more accurate results. The two most commonly used LA quantification
methods with cMRI data are adopted from methods accepted by the American Society of
Echocardiography as being accurate [49]. These methods are the area-length method and the serial short-
axis method.
5.3.1 Serial Short-Axis Method
The SSA method is considered the relatively more accurate method of quantifying the LA. In this
method, MRI images of the atrium are taken along the short-axis. These images are then contoured and
the summation of these contours is taken as the volume for the LA. It is due to this comprehensive nature
that the SSA method is considered the most reliable.
While it is indeed more comprehensive, this leads to an increased amount of time needed for
imaging and post-processing. Obtaining SA images is time intensive due to the number of images taken.
It also requires more breath-holds from subjects in the MRI which can be problematic when dealing with
cardiovascular pathologies. There is also an increased amount of time required in post-processing due to
the sheer number of images that need to be contoured in order to obtain volume data.
5.3.2 Area-Length Method
The AL method was developed as a less time and process intensive method for LA quantification.
Unlike the SSA, this method only requires a 2ch and a 4ch image. Contouring both sets of images
provides an area for each view. The model then assumes a prolate ellipsoid geometry for the LA and
calculates volume as:
83
∙∙
5.1
42
where A2ch and A4ch are the corresponding areas for each of the views, and L is the length of the LA
defined as the distance from the mitral annulus to the posterior LA wall [49]. As a value for L will given
from each of the 2ch and 4ch views, the shortest of these values is taken to be the atrial length. This
process is illustrated below in Figure 5.5.
This method, whilst being much less time consuming than the SSA does make some sacrifices in
regards to accuracy. The primary issue arises with determination for atrial length as there can be
inconsistencies. There is also the use of a prolate ellipsoid that may cause inaccuracies with the volume
determination. The LA is a more unorthodox shape and the use of such a geometry can result in
overestimation of volume. Lastly, it has been shown that the atrium assumes a more cylindrical shape as it
enlarges [50] and so the AL method may be unreliable in LA quantification for various pathologies.
(a) (b)
Figure 5.5: 2ch (a) and 4ch (b) used to calculate area and length. The LA area is represented in red with the white arrow showing the length of the atrium [51].
5.4 Proposed Virtual Short-Axis Method for Left Atrial Quantification
In this section, a virtual short-axis (VSA) method is proposed to find LA volume. This new
method is an attempt to balance the benefits of both the AL and SSA methods whilst minimizing the
issues that they both have. The VSA method uses only the 2ch and 4ch images, thus avoiding the time
consumption caused by acquiring and processing short-axis data. It also seeks to eliminate the error that
can arise from geometric assumptions like those of the AL method.
43
In this method, the contours from the 2ch and 4ch views are used as boundaries to create a series
of virtual short-axis elliptical discs. These discs are set at 0.5mm distances from each other. As the 2ch
and 4ch views are roughly orthogonal, corresponding diameters of the contours at the .5mm intervals are
set as the major and minor axes of the ellipse. The diameters are computed by use of a line from the mitral
annulus to the LA posterior wall which acts as the center. The diameters are calculated to be the width
across the contour at each interval perpendicular to that center. The areas are then summed to determine
the LA volume.
5.5 Validation of the Virtual Short-Axis Method
The VSA method while promising, does need to be validated. In order to do so, LA VTCs are
computed using each of the three aforementioned methods. Using the results of the SSA method as the
most accurate VTC's from the data from the AL and VSA methods are compared with relation to the SSA
results.
5.5.1 Method
The validation was conducted using nine healthy volunteers between the ages of 19 and 52. These
subjects presented with no known cardiac dysfunction at the time of cMRI. Auburn University IRB
approval was obtained for this study. Slices were taken in the 2ch, 4ch, and 6-8 slices along the short-axis
from the LA apex to a point approximately 1.5cm distal to the mitral annulus.
The MRIs were performed on a Siemens Verio 3T MRI scanner (Siemens, Erlangen, Germany).
A retrospectively-gated breath-hold balanced SSFP sequence was used. The parameters of the scan were:
an 8mm slice thickness, field-of-view of 36 x 40cm, a scan matrix 258 x 128, 40° flip angle, 5,4ms TR,
and 1.4ms TE.
Contours were manually drawn using custom in-house software at the ED and ES timeframes on
the 2ch, 4ch. and each of the slices in the short-axis views. These contours were then propagated to the
44
other timeframes using the method defined in Section 5.2.1. From here, LA VTCs were computed using
each of the three methods: the AL, SSA, and VSA method.
For the analysis, results from the SSA method were considered to be the gold standard. In order
to validate the VSA method, the hypothesis tested was that VTCs from the VSA method are closer to the
SSA VTCs than those computed by the AL method. This was done by computing the differences between
the two methods against the SSA: AL-SSA and VSA-SSA. Compound symmetry covariance structure
was applied to the differences and these were compared using mixed modeling. Finally, the absolute
differences were also compared using mixed modeling with applied compound symmetry covariance.
5.5.2 Results
Figure 5.6 shows the VTCs of each of the three methods averaged over the nine subjects. The
shapes of the VTCs are all qualitatively similar. The results from the comparison of the mean differences
of the AL and VSA methods from the SSA data are shown in Table 5.2. In Table 5.3, the least-squares
estimates of the difference between the absolute differences |VSA-SSA| and |AL - SSA| are displayed.
Figure 5.6: VTCs averaged over nine normal human volunteers computed using serial short-axis (SSA), area-length method (AL) and virtual short axis (VSA).
45
Table 5.2: Least-squares estimates of the mean differences between VTCs computed in ml using VSA and AL compared to SSA
Estimate
Standard Error
DF t Value Pr > |t| Alpha Lower Upper
AL-SSA -5.7 3. 8 24 -1.52 0.14 0.05 -13. 5 2.1
VSA-SSA -6.2 3. 8 24 -1.66 0.11 0.05 -14 1.5
Table 5.3: Least square estimate of the mean difference in ml between |AL-SSA| and |VSA-SSA| VTCs
|AL-SSA|-|VSA-SSA|
Estimate 6.8
Std Error 0.83
DF 8
t Value 8.12
Pr > |t| <.0001
Adjustment Tukey-Kramer
Adj P <.0001
Alpha 0.05
Lower 4.8
Upper 8.7
Adj Lower 4.8
Adj Upper 8.7
5.5.3 Discussion
From the least-squares estimates of the differences shown in Table 5.2, it is revealed that there is
no significant difference in either of these methods from the SSA method results. As the AL method has
been accepted as a valid method for LA quantification, it extends that as the VSA method produces VTCs
that are as significantly close to those from the SSA method as the results from the AL method, VSA is
also a valid method.
Meanwhile Table 5.3 illustrates that the absolute difference between the AL and SSA methods is
significantly higher than that found between the VSA and SSA methods. This shows that the VSA
method is potentially a more reliable method than using AL. This is also quantitatively evidenced by
46
Figure 5.6 where the mean VTC from the VSA method is closer to that of the SSA than the mean VTC
from the AL method.
It is important to note that while the SSA method was used as the standard for comparison, it has
not been validated against anatomical standard to claim it as a gold standard. There are concerns to be
raised as a 6-10mm slice thickness and the difficultly in defining the boundary between the pulmonary
veins and the LA in the short axis views. Therefore, there is a chance of misestimating the true atrial
volume. However, due to its comprehensive nature, it is considered a 3D technique and the most accurate
determination of LA volume using cMRI.
Therefore from this data, it can be said that the VSA method is effective in quantifying LA
volumes. It is more effective in its use of the 2ch and 4ch views than the AL method while still avoiding
the extra processing time required by the SSA method.
5.6 Conclusion and Further Work
In this section, a more effective method quantification method for the left atrium was sought. This
attempt came in two parts: the improvement of post-processing technique and a more effect method for
volume quantification.
The attempt to improve post-processing technique came in the application of a dual-contour
propagation method to more efficiently contour the LA. As contouring over all timeframes it very tedious
and time-intensive, the method would need only the ED and ES timeframes contoured manually, saving a
lot of time. While this method has been previously validated in the LV and RV, its effectiveness in the
LA had not been determined. However, through evaluation it has been found to indeed be an effective
propagation tool. This allowed for a quicker and more thorough testing of quantification methods.
The VSA method was introduced as a more effective alternative to the AL method for LA volume
quantification. While the AL technique eliminated the time-consuming use of short-axis contours, there
have been doubts as to the accuracy of its geometric assumptions. Through the use of the VSA method,
47
these geometric assumptions were eliminated and it was shown to be an effective method in LA
quantification.
It is important to note that these studies were all done using normal volunteers. While there was
some diversity in subject age, this was neither carefully controlled nor taken into account. As such, the
efficacy of both the propagation technique and the VSA method will need to be evaluated in regards to
subject age and with various pathologies. As the atrium is wont to remodel in both cases, the applicability
of these technique will need to be evaluated through further research. For further validation, comparison
of volumes calculated from this method with LA volumes for the same subject obtained using cardiac CT
would be beneficial.
48
Chapter 6
Summary and Future Work
The cardiovascular system plays an essential role in the human body. In order to get a
comprehensive perspective on the overall system, the individual components must first be characterized.
In this thesis, the quantification of two particular aspects of the cardiovascular system using cMRI was
discussed: blood flow in the arteries and left atrial volume.
With regards to blood flow in the arteries, prevalent time-domain based methods to quantify flow
through the use of PWV were discussed. The shortcomings in the use of these methods with PC MRI data
were presented and an alternative, frequency-domain based method for PWV determination was
examined. This method was shown to be more robust and reliable as it compensated for the relatively low
temporal resolution of PC MRI data.
In this thesis, LA quantification was approached in two ways: post-processing technique and
volumetric quantification methodology. In regards to post-processing, the applicability to a dual-contour
propagation method on the LA was evaluated. This technique, previously validated for the LV and RV,
was shown to be a viable method of contouring LA images. By reducing the manual tasks to solely
needing to contour the ED and ES timeframes, a lot of time can be saved in preparing the images for
quantification. Volumetric analysis of the LA was also explored. The AL and SSA methods, both adopted
for MRI use from echocardiography techniques, were discussed. The issues with the use of these
techniques were discussed and a novel VSA method was proposed. This method allowed for more
accurate quantification through the dismissal of inaccurate geometric assumptions while still minimizing
the number of cMRI images that need to be collected and processed. The VSA method was shown be a
valid method that can be more accurate in quantification than the AL method. It also holds promise in
regards to accurate quantification of remodeled atria.
It should be noted that the majority of this work was done using subjects who did not present with
cardiovascular dysfunction. However such issues, along with aging, change the physical and
49
physiological characteristics of cardiovascular anatomy. Therefore, the further applicability of all the
methods presented should be explored with regards to modified cardiac anatomy.
The work in this thesis is a portion of the groundwork for a more comprehensive characterization
of the cardiovascular system. Cardiovascular diseases and events are usually looked at in the specific
vessels and chambers. By analyzing the rest of cardiovascular system in addition to the specifically
affected one, a more complete perspective of cardiovascular interactions can be gleaned. In order to do
this, effective quantification methods for the other chambers and vessels should be pursued. While there
has been a lot of work on the ventricles, the contribution of the more peripheral structures such as the
atrial appendage can be quantified. When more complete quantification is done, the characteristics of
different structures can be compared and the interactions between the different anatomies can be more
specifically defined.
50
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